# Photon does not experience time

#### lvlastermind

This is a question that has been annoying me for quite some time. If a photon does not experience time then Doesn't that mean that a photon exists in only 3 dimensions? If so, then does that mean that other 3d objects can exist in our 4d space? What about an object that only has 2 dimensions? Can a 2d object exist in 4d space also?

Any clearing up on this topic would be appreciated.

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#### plover

Homework Helper
First, you'd need specify what you mean by "exists in only 3 dimensions". A photon inhabits the same 4d spacetime as any other object in our physical models.

If you mean "If you transform the reference frame to that of the photon, is the result a formally 3 dimensional space?", the question does not really work in Special Relativity as usually defined. The transform for reference frames requires that those frames be inertial. A rough definition for an inertial frame is that it is one where a specific observer is at rest. There is no rest frame for a photon under Relativity.

#### Goalie_Ca

I think what he means to say if that a photon's vector can be entirely described using a subspace of the vector space.

#### plover

Homework Helper
Under SR the path of a photon can be formally described as a segment of a one dimensional subspace (as long as the origin is defined appropriately so that a vector space structure works, spacetime is really more an affine space; so we'll assume that the origin is the 4d point where the photon is emitted). However there is no transform defined under SR that makes that 1d subspace either a space or a time axis for any inertial frame.

But (under SR) any inertial frame can be given a coordinate system that requires only the time dimension plus one space dimension to describe the path of a given photon.

#### lvlastermind

What I really mean is that if a photon is always at a constant c and therefor does not experience time; does that mean that a photon only has three dimensions?

keep in mind that im no physics expert

#### plover

Homework Helper
In the end, though it's probably unsatisfying, I think my first try is probably the answer to what you're asking:

"A photon inhabits the same 4d spacetime as any other object in our physical models."

But again I'm not entirely sure what you mean by "a photon only has three dimensions".

The question I've asked (and never really felt satisfied with the answers I've come up with) is "How would the universe appear if it could be observed from the perspective of a photon?" If I understand your question, it might be rephrased in these terms as: "If the universe were observed from the point of view of a photon, would it appear three dimensional?"

Part of the problem is that not only is there essentially no passage of time for a photon, but that mathematically, it would also appear that the photon would experience distances along its path of travel as contracted to zero. So one might say then that it takes the photon no time to travel because it finds that its starting point and its destination are the same place. So, in your terms, would that make the photon two dimensional?

In discussions that aren't accompanied by a mathematical framework, descriptions of relativity often emphasize that spacetime is "four dimensional". However, it is rarely mentioned in those discussions that the mathematics that is useful to describe 3 dimensions of space plus one of time has some important differences from what results from simply extending the ordinary conception of three dimensional space to four dimensions. The most obvious conception of "a four dimensional space" would, if used as a physical model, properly correspond to four "space-like" dimensions (as opposed to three "space-like" dimensions and one "time-like" dimension).

I hope this helps a little.

#### lvlastermind

plover said:
"If the universe were observed from the point of view of a photon, would it appear three dimensional?"
That is exactly the question I am trying to ask. Your answer is sufficient, thanks alot.

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